Study on the influence of bubble radius and volume fraction on sound wave velocity in seawater containing bubbles

Li Canping 1, Liu 2, Yang Li 3, He Jing 2, Lv Liangxin 2.

Li Canping (1977-), female, lecturer, doctor, mainly engaged in theoretical research and signal processing of scattered wave seismic exploration, e-mail: canpinglihydx @163.com.

Note: This paper was published in the third issue of Modern Geology (20 10), and this journal has some revisions.

1. School of Information, Guangdong Ocean University, Zhanjiang, Guangdong 524088.

2. School of Geophysics and Information Technology, China Geo University, Beijing 100083.

3. Northwest Branch of China Petroleum Exploration and Development Research Institute, Lanzhou 730020.

Based on the study of the sound velocity of seawater containing bubbles, the following conclusions are drawn: The relationship between bubble radius and seawater depth is that the bubble radius gradually increases with the shallower seawater depth. The relationship between sound velocity and bubble radius is that when the bubble volume fraction is small, with the increase of bubble radius, the sound velocity first increases gradually, then remains stable, and finally decreases slowly, with a small change range; When the bubble volume fraction increases gradually, the sound velocity increases with the increase of bubble radius, and the range of sound velocity varies with different bubble volume fractions. The relationship between sound velocity and bubble volume fraction is as follows: when the bubble volume fraction is small, the bubble volume fraction increases and the sound velocity decreases gradually; When the bubble volume fraction is large and the bubble radius is smaller than the critical radius, the bubble volume fraction increases and the sound velocity decreases gradually. When the bubble radius is greater than the critical radius, the bubble volume fraction increases, and the sound velocity first decreases and then gradually increases, and the range of sound velocity changes in different stages when the bubble volume fraction gradually increases.

Keywords: bubble radius; Bubble volume fraction; Natural gas hydrate; Seawater; speed of sound

Study on the influence of bubble radius and volume fraction on the sound velocity of seawater containing bubbles

Li Canping, Liu Xuewei, Yang, Jing He, Lu Liangxin

1. School of Information, Guangdong Ocean University, Zhanjiang, Guangdong 524088.

2. School of Geophysics and Information Technology, China Geo University, Beijing 100083.

3. Petroleum Exploration and Development Research Institute; China Petroleum Northwest Development Company. Lanzhou, China 730020

Abstract: Based on the study of the sound velocity of seawater with bubbles, the following conclusions are drawn. The relationship between bubble radius and seawater depth is that the shallower the seawater, the larger the bubble radius. The relationship between sound velocity and bubble radius is that when the bubble volume fraction is small, with the increase of bubble radius, the sound velocity first increases gradually, then remains unchanged, and finally decreases slowly, with little change in sound velocity. When the volume fraction of bubbles increases gradually, the sound velocity increases with the increase of bubble radius, and the amplitude of sound velocity changes with different bubble volume fraction. The relationship between sound velocity and bubble volume fraction is that when the bubble volume fraction is small, the sound velocity gradually decreases with the increase of bubble volume fraction. When the bubble volume fraction is large and the bubble radius is smaller than the critical radius, the sound velocity decreases gradually with the increase of the bubble volume fraction; When the bubble radius is greater than the critical radius, with the increase of bubble volume fraction, the sound velocity first decreases and then gradually increases. In addition, the variation range of sound velocity is different in each state where the bubble volume fraction increases.

Keywords: bubble radius; Volume fraction of bubbles; Gas hydrate; Seawater; speed of sound

Introduction to 0

Natural gas hydrate is a solid substance, which mainly exists in permafrost and seabed sediments. There are huge natural gas hydrate resources on the earth, of which the natural gas hydrate in the ocean accounts for the vast majority, and the natural gas hydrate resources in the South China Sea reach 67 billion t oil equivalent [1]. From April to June, 2007, gas hydrate drilling was carried out in Shenhu sea area on the northern slope of South China Sea, and gas hydrate samples were obtained [2].

Submarine natural gas hydrate overflows into seawater in the form of bubbles through migration channels such as pores and fractures. Many places in the world have discovered the phenomenon of bubbles escaping from the seabed through photography, video recording or acoustic recorder. Eberhard J.Sauter[3] and others recorded the photos of methane bubbles escaping from submarine hydrate in the north of the center of Hakon mosby Mud Volcano (HMMV) on the western edge of Barents Sea. Texas A&M University. In 2002, the Institute of Ocean Drilling of M University detected the methane bubble seawater plume overflowing from the seabed hydrate with an acoustic recorder [4]. S. Garcia-Gil de et al. [5] found the acoustic plume and cloud disturbance formed by bubbles in seawater in the shallow gas escape zone ("boiling zone" formed by bubbles escaping from the water surface), and recorded the beaded reflection signal in the shallow gas escape zone along the Caspian Sea [6]; In the investigation of hydrate in the Sea of Okhotsk in central Russia and China, the "flame" reflection of bubbles generated by hydrate decomposition was detected [7]. Gu Zhaofeng and others [8] found in the geological survey of the South China Sea that the shallow seismic profile recorded a large number of speckled reflections distributed in seawater. Bubbles in water will scatter seismic waves and respond on seismic profiles. Imaging the scattered waves can detect plumes in water.

The existence of bubbles in seawater will inevitably affect the sound speed of seawater, and then respond to the seismic profile of natural gas hydrate detection. Yao [9] studied the influence of bubbles on sound propagation, gave the expression of sound velocity in the medium containing bubbles, and studied the relationship between bubble volume fraction and sound frequency, but did not study the influence of bubble volume fraction and bubble radius on sound velocity in detail. Based on the velocity model of water containing bubbles proposed by Yao, the variation of sound wave propagation velocity in seawater containing bubbles is discussed in detail from two aspects: bubble volume fraction and bubble radius. Because there are many factors controlling the gas source of natural gas hydrate, it is necessary to distinguish it with comprehensive indicators [10]. This paper lays a foundation for further research on the gas source of submarine natural gas hydrate.

1 speed of sound in water with bubbles

The dissolved gas in the liquid and bubbles generated during cavitation will change the pressure distribution in the liquid [1 1], thus changing the acoustic characteristics of the liquid. Yao [9] takes the sound pressure and radial vibration velocity at the bubble wall as boundary conditions, and derives the expression of sound velocity in the medium containing bubbles:

Enrichment Law and Exploitation Basis of Natural Gas Hydrate in South China Sea

Where: cm is the sound speed of gas-liquid mixture, m/s; K is liquid bulk modulus, n/m2; Kb is the gas bulk modulus, n/m2; ρ is the density of liquid, kg/m3; ρb is the gas density, kg/m3; ω is the frequency, Hz; A is the bubble radius, m; σ is the surface tension of liquid, n/m2; R is the radius when the bubble-containing two-phase mixing zone is assumed to be spherical, m; φ is the volume fraction of bubbles, that is, the volume fraction of bubbles in a spherical region with a radius of R. When R is fixed, this parameter is determined by the number and size of bubbles. In the derivation of this formula, the secondary factors such as heat conduction are ignored, and it is assumed that the bubbles in the two-phase mixing zone with bubbles have the same radius [9].

In the formula (1), k, Kb, ρ, ρb and σ are fixed parameters, and ω, a, φ and r are given variable parameters. Therefore, given the above parameters, the sound velocity of seawater containing bubbles with different bubble radii and different bubble volume fractions can be calculated by this formula.

2 Bubble radius changes with seawater depth

In the process of gas hydrate bubbles overflowing from the seabed rising from the seabed, the bubble radius will increase with the decrease of pressure, that is, the bubble radius is related to the depth of seawater. Zhu [12] gave the formula of bubble radius changing with depth when studying the acoustic scattering law of wake bubbles:

Enrichment Law and Exploitation Basis of Natural Gas Hydrate in South China Sea

The formula assumes that there is no heat exchange between bubbles and surrounding media, ignoring the influence of gas diffusion. According to the first law of thermodynamics, the value of PVλ is constant during the movement of bubbles. Knowing the radius R0 of bubbles at the initial depth z0, we can infer the radius r at a certain depth z.. Where the seawater density p =1.023kg/m3; The surface tension of seawater σ = 0.0738 N/m; g = 9.8n/m； Sea surface atmospheric pressure P0 =1.0135×105pa; The specific heat ratio of air λ= 1.4.

According to formula (2), by substituting the above parameters, the initial depth (1 350 m) and radius size (2. 1× 10-3m) of the bubbles overflowing from the seabed can be given, and the change of bubble radius with seawater depth can be calculated, as shown in figure 1.

Figure 1 shows the same law and theory, that is, with the decrease of seawater depth and pressure, the bubble radius will increase. According to this law, we can further study the influence of bubble radius on sound wave velocity at different seawater depths.

Figure 1 Relationship between bubble radius and seawater depth

3 the influence of bubble radius on the sound speed of seawater

According to literature [3], the bubble radius of gas hydrate escaping from the deep seabed ranges from 5.0× 10-4 to 5.0× 10-3m. Considering that there are still some tiny bubbles in the actual situation, in order to study the change of sound velocity in seawater with smaller bubbles, the bubble radius is set to 5.0× 10-. According to the formula (1), given the parameter value, K = 2.34× 109N/m2, KB = 1.4× 105N/m2, P = 1.023kg/m3. R= 1.0 m, and the variation of sound wave velocity with different bubble volume fractions within the radius of 5.0×10-5 ~ 5.0×10-3 m is calculated, as shown in Figure 2.

Relationship between sound wave velocity and bubble radius in seawater with bubbles.

As can be seen from Figure 2, within the bubble radius range of 5.0×10-5 ~ 5.0×10-3m, the sound velocity presents two modes: First, when the bubble volume fraction is small, as shown in Figures 2a and b, with the increase of bubble radius, the sound velocity gradually increases, then remains stable, and finally slowly decreases, with a small range of sound velocity change. 2. When the bubble volume fraction increases gradually, as shown in Figure 2c-F, with the increase of bubble radius, the sound velocity increases gradually, and the range of sound velocity varies with different bubble volume fractions.

When the bubble volume fraction is small, as shown in Figure 2c, with the increase of bubble radius, the sound velocity gradually increases, but the sound velocity has little change, with the increase range of 3 m/s and the range of186 ~189 m/s; In fig. 2 d, with the increase of bubble radius, the sound velocity gradually increases, and the sound velocity changes greatly, with the increasing range of 12 m/s and the changing range of100 ~12 m/s. With the increase of bubble volume fraction, as shown in fig. 2e, the bubble volume fraction is/. The volume fraction of bubbles ranges from 60% to 80%, from 40 to 280 m/s, from 90% to 100% and from 0 to 450 m/s. ..

Figure 2e-f has common characteristics: when the radius is less than 2.0× 10-3m, the bubble volume fraction is large and the velocity is small; When the radius is greater than 2.0× 10-3m, the larger the bubble volume fraction, the greater the velocity. And the range where the two lines intersect in fig. 2f is relatively wider than that in fig. 2e. It can be concluded that there is a critical radius rc, that is, rc=2.0× 10-3m. When the bubble volume fraction is large (more than 5%) and the bubble radius is less than the critical radius rc, the sound speed decreases gradually with the increase of the bubble volume fraction. When the bubble radius is greater than the critical radius rc, the sound velocity increases with the increase of bubble volume fraction. This is because when the bubble volume fraction is constant, the number of bubbles will decrease with the increase of bubble radius, and then the influence on the sound speed of seawater will decrease, so the sound speed of gas-liquid mixture will increase with the increase of bubble radius.

4 Effect of bubble volume fraction on sound velocity of seawater

Because the volume fraction of bubbles in question varies greatly, ranging from 0.0005% to 100%, the volume fraction of bubbles is divided into the following five parts to study the change of sound wave velocity: 1 part is that the volume fraction of bubbles varies from 0.0005% to 0.005%; The second part is that the bubble volume fraction changes between 0.005% and 0.05%; The third part is that the bubble volume fraction changes between 0.05% and 0.5%; The fourth part is the change of bubble volume fraction from 0.5% to 5%; The fifth part: the change range of bubble volume fraction% 1 ~ 100%; The volume fraction of these five parts is constantly changing.

As before, given the parameter value in the formula (1) and the bubble radius, the radius is selected in the range of 0.005% ~ 0.5% m, and the sound velocity change of gas-liquid mixture with different bubble volume fraction is calculated, as shown in Figure 3.

As can be seen from Figure 3, with the increase of bubble volume fraction, the sound velocity of gas-liquid mixture forms two change modes: First, when the bubble volume fraction is less than 5%, the sound velocity gradually decreases with the increase of bubble volume fraction in the bubble radius range of 5.0×10-5 ~ 5.0×10-3m, as shown in Figure 3a-d; Second, when the bubble volume fraction is greater than 5%, the sound speed gradually decreases with the increase of the bubble volume fraction within the bubble radius range. When the bubble radius is greater than the critical radius rc=2.0× 10-3m, the sound speed first decreases and then gradually increases with the increase of the bubble volume fraction, as shown in Figure 3f. At different stages when the volume fraction of bubbles gradually increases, the amplitude of sound velocity decrease and the amplitude of sound velocity change are different, which are as follows:

In the 1 section, the volume fraction of bubbles varies from 0.0005% to 0.005%. As shown in Figure 3a, with the increase of the volume fraction of bubbles, the sound speed linearly decreases by about 350 m/s, ranging from 1 100 to1450 m/s. ..

In the second part, the volume fraction of bubbles changes from 0.005% to 0.05%, as shown in fig. 3b. With the increase of bubble volume fraction, the sound velocity decreases in an arc shape, with a large decrease range of about 600 m/s, ranging from 500 ~1100 m/s.

In the third part, the change range of bubble volume fraction is 0.05% ~ 0.5%, as shown in Figure 3c, with the increase of bubble volume fraction, the sound speed decreases in an arc shape, with the decrease range of about 300 m/s and the change range of 200 ~ 500 m/s. ..

In the fourth part, the change range of bubble volume fraction is 0.5% ~ 5%. As shown in Figure 3d, with the increase of bubble volume fraction, the sound speed decreases in an arc shape, with a small decrease range of about 90 m/s, ranging from100 ~190 m/s.

In the fifth part, the volume fraction of bubbles changes from 1% to 100%, as shown in Figure 3e, with the increase of the volume fraction of bubbles, the sound speed decreases rapidly at first, and then slowly, with a decreasing range of about 150 m/s; As shown in fig. 3f, with the increase of bubble volume fraction, the sound velocity first decreases and then gradually increases, and the range is100 ~ 450 m/s.

In fig. 3f, the velocity decreases first and then increases gradually during the change of bubble volume fraction, indicating that the physical properties of the original medium will be significantly changed by adding a small amount of gas into seawater or adding a small amount of seawater into the gas [13], and its density, compressibility and other physical properties will change, resulting in the change mode of velocity decreasing first and then increasing.

Relationship between sound wave velocity and bubble volume fraction in seawater containing bubbles.

In Figure 3a-e, with the increase of bubble volume fraction, the sound velocity in seawater gradually decreases, because the sound velocity in liquid gradually becomes the sound velocity in gas.

5 abstract

1) In the process of gas hydrate bubbles overflowing from the seabed rising from the seabed, the relationship between bubble radius and seawater depth is that as the seawater depth becomes shallow, the bubble radius gradually increases, and the change of bubble radius will have an impact on the sound speed of seawater.

2) The relationship between sound velocity of gas-liquid mixture and bubble radius and bubble volume fraction is as follows:

A. The bubble radius ranges from 5.0×10-5 to 5.0×10-3m. With the increase of bubble radius, the sound velocity presents two modes: first, when the bubble volume fraction is small, the sound velocity increases gradually, then remains stable, and finally decreases slowly, with a small change range; Secondly, when the volume fraction of bubbles increases gradually, the sound velocity also increases gradually, and the range of sound velocity changes with the volume fraction of bubbles.

B. With the increase of bubble volume fraction, the sound velocity forms two change modes: First, when the bubble volume fraction is less than 5%, the sound velocity gradually decreases within the bubble radius of 5.0×10-5 ~ 5.0×10-3m. Secondly, when the volume fraction of bubbles is more than 5%, the sound velocity will gradually decrease within the bubble radius range of 5.0×10-5 ~10-3m, that is, when it is less than the critical radius rc=2.0× 10-3m; When the bubble radius is larger than the critical radius rc=2.0× 10-3m, the sound speed first decreases and then gradually increases. At different stages when the bubble volume fraction gradually increases, the amplitude of sound velocity decrease and the amplitude of sound velocity change are different.

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